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Mass Rate or Vol Rate Conservation

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Old   April 22, 2021, 16:26
Default Mass Rate or Vol Rate Conservation
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Hello,

I'm simulating a room filled with Gas 1. Gas 2 is being injected with a constant mass rate. There is an opening in the room which allows the gases to scape. The gases have different densities. I'm running transient.

From continuity equation, I expect that at each time step the mass rate that enters should exit (i.e. ṁg2 = Ṁg1 + Ṁg2). However, the CFD simulation shows that the volumetric flow rate is being conserved (i.e. ṁg2/ρg2 = Ṁg1/ρg1 + Ṁg2/ρg2). Looking in the solver, both gases have a mass imbalance % of zero.

Eventually, once stated state condition is reached, the entire mass rate of Gas 2 that enters, exists (i.e. ṁg2 =Ṁg2 and Ṁg1 = 0). But my question is for the initial transient solution where instead of mass flow rate, volumetric flow rate is being conserved. Is this something that one should expect?

Thanks in advance for any help on this.
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Old   April 22, 2021, 19:10
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This is exactly what you would expect. Assuming this is all a constant pressure process, then volume flow rate is conserved (as you found), but because gas 1 and 2 are different gases with different gas constants (R), then the cooling of gas 2 and heating of gas 1 will affect the overall density of the gas in the room, at least during the initial transient. This means the gas 2 mass flow in will not equal the mass flow out initially, but after a while when it reaches a steady state it will.
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